"to eat either" is a correct and usable phrase in written English.
It can be used in a sentence to indicate a choice between two options for eating. Example: I am not sure what to make for dinner tonight. What would you like to eat either, pasta or chicken?.
I would be happy to eat either dish once a week.
One human study involved 30 menopausal women randomized to eat either cookies with lion's mane extract or placebo cookies without the extract for a month.
"If you help get them sick and they are unable to work, they are not going to go out to eat, either".
If eating meat was a crucial, unavoidable part of the human diet, it would be another matter – but, quite clearly, there is no health requirement whatsoever to eat either meat or fish.
'I always point out to people that when they're cooking for a dinner party they don't want to eat either.' Yes, but most of us only do that every now and then, not every day.
Take leftover baked beans for a packed lunch, to eat either hot or at room temperature and sprinkled into a salad with tomatoes, celery, fresh herbs and a good vinaigrette.
I said he would have to have eaten either shit or human flesh for us to do that.
"But nobody's going to eat those either," he said.
When we sat down to eat he either read the paper or gazed into the distance.
("She tried to remember what she had planned to eat for either lunch or dinner and found her way back into the living room, where she sat down in front of the television set. She saw, reflected in the dark screen, herself, in black-and-white, miniaturized").
They don't have to eat it either, living in a home where it's constantly present in the air is often enough to affect them.
